Many storage systems are configured to include multiple storage tiers, with different ones of the tiers providing different levels of input-output (JO) performance or other characteristics. In such systems, data may be moved from one tier to another within a given storage system based on access frequency of the data or other factors. For example, some systems are configured to utilize multiple storage tiers having different types of disk drives in order to improve performance while reducing cost. This is achieved by putting the more active (“hot”) data on faster but more expensive disk drives and the less active (“cold”) data on slower but cheaper disk drives. Such an arrangement is a type of fully automated storage tiering (FAST). Data can also be moved between storage tiers in conjunction with a planned migration from one storage system to another storage system. For example, in such a migration context, the tiers may comprise respective storage arrays in different storage systems.